You need to get the transfer agents involved. Each public company's stock transactions (buys, sells, owners (actual name not broker name) of record, borrowers of record, etc.) should go through the transfer agents server so the company can watch over its own stock. Computers and the internet make this record keeping easy and not a burden on the transaction cycle.

Stock is money. It needs to be serial numbered (electronic and paper), tracked, debited and credited, and closed out every night just like money is.